When a continues tone image such as a silver salt photo is reproduced by an electrophotographic apparatus or method, the continuous tone image is usually expressed by the area ratio of the toner deposited area (image area) to the toner non-deposited area (background area) in each of very small regions formed on an image receiving sheet such as paper (the rate of the image area to the area of each small region is called the image area rate). The technique of two-dimensionally recording the data of a continuous tone image, as an image of two levels (e.g., ON and OFF) on a latent image bearing member is called image binarization.
For the image binarization, which is also called halftoning, to reproduce the gray scale of a continuous tone image, many methods are proposed. In this technique, continuous gray scale densities are converted, for example, into a geometric distribution of two-value dots.
For halftoning, two major methods are proposed; "amplitude modulation screening method" and "frequency modulation screening method".
In the amplitude modulation screening method, usually the halftone dots are formed in fixed regularly arranged geometric grids. In other words, in this method, in each region with a finite density, the halftone dots are modulated in size to reproduce the corresponding gray scale density, while the dots number is invariable. A typical technique is Fattening type dither technique called dot concentration type technique. FIG. 3(a) shows an example of its binarization model.
On the other hand, in the frequency modulation screening method, the distance between halftone dots, or the number of halftone dots formed per unit area is mainly modulated to express a continuous tone image. A typical technique is error diffusion technique. FIG. 3(b) shows an example of its binarization model.
Low resolution printers of 1/12 mm or more in the minimum dot pitch, especially ink jet printers generally use the frequency modulation screening method. In the amplitude modulation screening method, for example, in the Fattening type dither technique, an entered density value is compared with the threshold consisting of an m.times.m matrix, and the ON or OFF of each dot (that is, whether or not an image area is formed in the corresponding dot of the matrix) of many halftone dots is decided. Thus, if the gray scale expressibility, i.e., the number of gray scale levels is increased, then the threshold matrix becomes larger. In this case, the pitch of geometric grids as gray scale expression units becomes larger, and the expressibility of the detail is lowered correspondingly. That is, the relative resolution (a high relative resolution means that the minimum pitch of independently formed halftone dots is small; in the amplitude modulation screening method, it refers to a case where the pitch of geometric grids is small) is in a trade-off relation with the gray scale expressibility.
In a low resolution printer, detail reproducibility cannot be enhanced especially due to the trade-off relation.
Accordingly, in a low resolution printer, the frequency modulation screening method such as the error diffusion technique is used since it can enhance the apparent relative resolution (in the frequency modulation screening method, the relative resolution can be evaluated almost in reference to the maximum pitch of formed single dots).
On the other hand, medium resolution printers of 1/15 mm or less in the minimum pitch of dots, in particular electrophotographic printers have rather adopted the amplitude modulation screening method because of a phenomenon called "dot gain". The dot gain refers to a phenomenon that when the pixels calculated from a resolution, i.e., the halftone dots of an ideal size are formed on the image receiving sheet such as paper, the actually obtained optical density is higher than the ideal optical density to be obtained. For example, when the image area rate on binary image data in a certain region is 50%, the ideal optical density is equal to the central value between that of a region with no dot formed at all (image area rate 0%) and that of a region filled with dots (image area rate 100%) (to be more strict, ideally the average light reflectance or transmission factor of the region is equal to the central value), but the actual optical density may become slightly higher than the ideal value. This is called dot gain. This occurs mainly according to the following principles.
The dot gain in an electrophotographic printer can be roughly classified into (1) mechanical dot gain, (2) optical dot gain and (3) the dot gain attributable to the single dot shape. The mechanical dot gain (1) refers to a phenomenon that when a toner is transferred from a latent image bearing member onto an image receiving sheet such as paper or onto an intermediate transfer member, or from an intermediate transfer medium onto an image receiving sheet, the pressure applied mainly or as an auxiliary means acts to press the toner layer in the thickness direction, to slightly crush the toner layer, for widening the halftone dots.
The optical dot gain (2) refers to a phenomenon that since the toner layer transferred onto paper has a finite thickness, the light incident on the paper surface in the direction inclining to the normal line of paper surface is partially intercepted by the toner layer, to form a shadow, without reaching part of the paper surface intended to be irradiated with the light, thus lowering the average reflectance of light, to raise the observed optical density.
The dot gain attributable to the single dot shape (3) is a phenomenon often observed, for example, with an electrophotographic apparatus of the type to form a latent image on a latent image bearing member by irradiation with a laser beam, etc., in which image areas are formed in the regions irradiated with the beam (white-black mode development type), and refers to a phenomenon that the area of each halftone dot increases since the shape of the corresponding single dot actually formed on the latent image bearing member does not agree with the theoretical shape of each single dot in binary image data. The reason why this occurs is that since the binary image data divide the surface of the latent image bearing member into square matrixes, the data express whether or not toner deposited regions are formed at the square dot positions, while in the actual latent image formation, the shape of the laser beam spot, etc. mostly gives a pattern including the square (for example, a circle with the square inscribed, etc.) to cover each square dot position (when the shape of the beam spot, etc. is not a square, regions of 100% in image area rate cannot be formed without adopting this configuration). Hence, for example, when a minimum circular dot to cover a square dot position is used as a single dot, the actual image area rate of the latent image is about 1.5 times the image area rate on binary data.
The dot gain occurs at the boundary region between an image area with the toner deposited and a background area with no toner deposited, as can be seen from the above mentioned principles. Therefore, as shown in FIG. 3, in the frequency modulation screening method larger in the boundary region than the amplitude modulation screening method, the dot gain becomes larger, and the gray scale reproducibility tends to decline especially in medium to high density regions. This tendency is pointed out also in Erwin Widmer et al.'s paper, TAGA, 28-43 (1992).
In the dry electrophotography, since toner particles large in average particle size are used for development in most cases, the toner layer of the toner image is thick, to especially emphasize the phenomenon of dot gain. Moreover, in the frequency modulation screening method, it is said that in the regions low in image area rate, since the dot pitches are extremely large, the rough feeling called graininess cannot be avoided. For these reasons, electrophotographic apparatuses with a medium to higher resolution have been adopting the amplitude modulation screening method.
However, the amplitude modulation screening method has a serious disadvantage called "moire". This is an undesirable pattern caused when halftone dots are formed on regularly arranged geometric grids in a halftoned image. The moire can be classified into subject moire, color moire, etc., depending on causes.
The subject moire is caused by the geometric interaction between the periodic image area rates in the original image such as an image expressing the texture of a textile fabric and the pattern of said geometric grids.
The color moire is caused by the interference between the binary images of respective colors respectively with the above mentioned periodicity occurring when the binary images of respective colors obtained by converting a color image are overlapped on one image receiving sheet. In particular, the color moire caused when three or more binary images are overlapped is called "rosette" pattern.
Moreover, in the amplitude modulation screening, if the number of gray scale levels is increased, the relative resolution also declines. Consequently, even with an electrophotographic apparatus very high in resolution, it is difficult to obtain a toner image with large number of the gray scale levels and with high relative resolution. In addition, the above mentioned problem of moire could not be solved fundamentally.